2P would be twice the peroid, I could tell because it would be twice as long.

The waveform would stretched out further horizontally due to it having to take more time to elapse.

I can tell I'm missing the fundamental insight that should arise from this question, can you be more blunt?

When we say "the" period of a periodic function is P, we usually mean that P is the smallest positive value such that f(x+P) = f(x) for all x. However it is correct to say any Q > 0 that has the property that f(x+Q) = f(x) is a period of the function also. It just may not be the smallest period. After all, if a function repeats every 2 units, wouldn't also repeat every 4 units? If f has period P, what do you get if you calculate ##f(x+2P) = f((x+P)+P)=?##

Staff: Mentor

2P would be twice the peroid, I could tell because it would be twice as long.

Neatly sketch a large sinusoid across a sheet of squared paper. Now, on the same axis, sketch another sinusoid, but draw this one of smaller amplitude and show it having exactly 4 cycles within the time of the first one having just one cycle.

Underneath these, sketch their sum.

Try some more sketches. Try it again, but this time make the first one of smaller amplitude and the second one the larger.